Summary: We propose an extended version of the classical Karhunen-Loève expansion of a multivariate random process, termed a normalized multivariate functional principal component (\(m\mathrm{FPC}_n\)) representation. This takes variations between the components of the process into account and takes advantage of component dependencies through the pairwise cross-covariance functions. This approach leads to a single set of multivariate functional principal component scores, which serve well as a proxy for multivariate functional data. We derive the consistency properties for the estimates of the \(m\mathrm{FPC}_n\), and the asymptotic distributions for statistical inferences. We illustrate the finite sample performance of this approach through the analysis of a traffic flow data set, including an application to clustering and a simulation study. The \(m\mathrm{FPC}_n\) approach serves as a basic and useful statistical tool for multivariate functional data analysis.